Generates a forecast of future values of a time series
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality. Exponential smoothing is often used for analysis of time-series data.
Exponential smoothing is one of many window functions commonly applied to smooth data in signal processing, acting as low-pass filters to remove high-frequency noise. This method is preceded by Poisson's use of recursive exponential window functions in convolutions from the 19th century, as well as Kolmogorov and Zurbenko's use of recursive moving averages from their studies of turbulence in the 1940s.
The raw data sequence is often represented by beginning at time , and the output of the exponential smoothing algorithm is commonly written as , which may be regarded as a best estimate of what the next value of will be. When the sequence of observations begins at time , the simplest form of exponential smoothing is given by the formulas:[1]
where is the smoothing factor, and . If is substituted into continuously so that the formula of is fully expressed in terms of , then exponentially decaying weighting factors on each raw data is revealed, showing how exponential smoothing is named.
The simple exponential smoothing is not able to predict what would be observed at based on the raw data up to , while the double exponential smoothing and triple exponential smoothing can be used for the prediction due to the presence of as the sequence of best estimates of the linear trend.
^Cite error: The named reference NIST was invoked but never defined (see the help page).
and 26 Related for: Exponential smoothing information
Exponentialsmoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function...
has media related to Moving averages. Exponentialsmoothing Local regression (LOESS and LOWESS) Kernel smoothing Moving average convergence/divergence...
distributions of a certain form Exponentialsmoothing, a technique that can be applied to time series data Exponential type Exponential type or function type,...
smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing....
applying a triple exponentialsmoothing which is not the case. The name triple comes from the fact that the value of an EMA (Exponential Moving Average)...
applying a double exponentialsmoothing which is not the case. The name double comes from the fact that the value of an EMA (Exponential Moving Average)...
sequence ExponentialsmoothingExponential stability Exponential sum Exponential time Sub-exponential time Exponential tree Exponential type Exponentially equivalent...
also outside this scope. Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions...
distribution The exponential distribution, which describes the time between consecutive rare random events in a process with no memory. The exponential-logarithmic...
{\displaystyle \textstyle [0,\infty )} . The failure process with the exponentialsmoothing of intensity functions (FP-ESI) is an extension of the nonhomogeneous...
Holt's model. An ARIMA(0, 1, 1) model without constant is a basic exponentialsmoothing model. An ARIMA(0, 2, 2) model is given by X t = 2 X t − 1 − X t...
and a dashed mid-line at 50. Wilder recommended a smoothing period of 14 (see exponentialsmoothing, i.e. α = 1/14 or N = 14). Wilder posited that when...
period demand, simple and weighted N-Period moving averages, simple exponentialsmoothing, Poisson process model based forecasting and multiplicative seasonal...
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special...
future values. One example of an ARIMA method is exponentialsmoothing models. Exponentialsmoothing takes into account the difference in importance between...
and GARCH errors. Exponentially weighted moving average (EWMA) is an alternative model in a separate class of exponentialsmoothing models. As an alternative...
of the graph indicating an observed failure time. The smooth red line represents the exponential curve fitted to the observed data. A graph of the cumulative...
=g^{-1}(\eta )} . An overdispersed exponential family of distributions is a generalization of an exponential family and the exponential dispersion model of distributions...
regression local regression multivariate adaptive regression splines smoothing splines neural networks In Gaussian process regression, also known as...